CPhill

(x + 5)^2  + 3 =   28            

(x + 5)^2  = 28   - 3

(x + 5)^2 =  25              take both roots

x + 5 =    sqrt (25)                     x + 5 =  -sqrt (25)

x +  5  =  5                               x +  5   =  -5

x =  0                                        x  =  -5 - 5  =   -10

x =  -10 , 0

P(first selected is blue)  * P( second selected is blue )   =

4/ 9  *   3 /  8   =

12 / 72   =

1 /  6

y =  (1/2)  ( x - 2)  - 3

y = (1/2)x  - 1  -  3

y = (1/2) x  -  4

The y intercept  is   -4

Darn, CentsLord....you're  making me look bad  .....LOL!!!!!!

Good job  !!!!

Here's my best attempt  !!!

Look at  the "ones" digit......let's suppose it is  "1"

Then...we  have   4!  = 24  ways  to  arrange  the  other leading digits with  each 5 digit integer ending in "1"

And it will  be  the same for each of the other integers ending in 3, 4 , 5 or 6

So  the  sum  of  the  digits in the "ones"  place will  be

24  ( 1 + 3 + 4 + 5 + 6)  =  456

And   the same  will  happen  in the "tens,"  "hundreds," "thousands," and "ten thousands"  places

So....the  sum will be

456  ( 1  + 10  + 100 + 1000  +  10000)  =

456  ( 11111)   = 

5,066,616

Sorry...slight error...I  figured  for 5 questions instead of 4....see my corrected answer

BC is  the height of triangle  BCD

So

80   = (1/2) CD * BC

160 = 15 * BC

160 / 15  = BC = 32/3

And ABCD is a trapezoid...so its area  =

(1/2) BC *  ( AB + CD)  =

(1/2) (32/3)  ( 9 + 15)  =

(1/2) ( 32/3) (24)  =

128

So....area of triangle BAD =  [ABCD  ] - [ BCD ] =   128  -  80   =   48

(Binomial) Probability  =   1  -  probability  that  he gets none correct  =

1 -  (4/5)^4   =

369/ 625  ≈ 

59%

CORRECTED.....

The altitude is opposite a 60°  angle

The  side  length =  (2 / sqrt 3) * altitude  =  (2 / sqrt 3)  * 27 =   54/sqrt 3  =  18 sqrt 3